CPM Homework Help : PC3 Problem 6-19

Given $f(x)=2x+3$ and $g(x)$ as defined by the table at right, evaluate each of the following expressions.

$\frac { g ( - 3 ) } { f ( 1 ) }$
Step (a):
$g\left(−3\right) = 3$
$f\left(1\right) = 2\left(1\right) + 3$

$f(2)+g(2)$

Step (b):

$f\left(2\right) = 2\left(2\right) + 3$
$g\left(2\right) = 1$

$f(g(2))$
Step (c):
$f\left(1\right)$

$g(f^{−1}(−1))$
Hint (d):
To determine the value of $f^{−1}\left(1\right)$ , solve $−1 = 2x + 3$ for $x$ .

$f(g^{−1}(0))$
Hint (e):
To determine the value of $g^{−1}\left(0\right)$ , solve $g\left(x\right) = 0$ for $x$ .

$g^{−1}(f(−3))$
Step (f):
$g^{−1}\left(2\left(−3\right) + 3\right)$

$\left. \begin{array} { | c | c | } \hline x & { g ( x ) } \\ \hline - 3 & { 3 } \\ \hline - 2 & { - 3 } \\ \hline - 1 & { 2 } \\ \hline 0 & { 1 } \\ \hline 1 & { - 2 } \\ \hline 2 & { 1 } \\ \hline 3 & { 0 } \\ \hline \end{array} \right.$